Prediction of internal pressure profile of compression bandages using stress relaxation parameters

Biorheology 49 (2012) 1 13 1 DOI 10.3233/BIR-2012-0601 IOS Press Prediction of internal pressure profile of compression bandages using stress relaxation parameters Bipin Kumar, Apurba Das and R. Alagirusamy Department of Textile Technology, IIT Delhi, New Delhi, India Received 20 December 2011 Accepted in revised form 13 February 2012 Abstract. The efficacy of compression therapy using compression bandages is highly dependent on the level of compression applied and the sustenance of the pressure during the course of treatment. This study attempts to predict the pressure profile generated by compression bandages using constitutive equations describing relaxation behavior of viscoelastic materials. It is observed that this pressure profile is highly correlated with the stress relaxation behavior of the bandage. To model the pressure profile, the stress relaxation behavior of compression bandages was studied and modeled using three mechanical models: the Maxwell model, the standard linear solid model and the two-component Maxwell model with a nonlinear spring. It was observed that the models with more component values explained the experimental relaxation curves better. The parameters used for modelling relaxation behavior were used to describe the pressure profile, which is significantly dependent on the longitudinal stress relaxation behavior of the bandage, using the modified Laplace s law equation. This approach thus helps in evaluating the bandage performance with time during compression therapy as novel wound care management. Keywords: Viscoelasticity, wound care, modeling, venous ulcers, mechanical models 1. Introduction Compression therapy remains the cornerstone component in the management of both venous and lymphatic disease. Compression therapy aims to increase venous and lymphatic return, reducing oedema and venous pressure in the limb [10,11,19]. Bandaging systems are recommended during the therapy phase of treatment and are suitable for compression therapy in venous leg ulcers and to significantly reduce oedema [11,12,19]. The pressure is generated in the interface between bandage and skin because of compression by a bandage during wrapping the bandage around the limb by the application of external force. This pressure is called interface pressure [11]. The interface pressure produced by any compression bandaging system depends on the complex interaction of many factors the bandage properties, the limb shape and size, the application technique and the physical activity taken by the patient [8,10,11]. The effectiveness of the therapy is highly dependent on the level of compression and the sustenance of the interface pressure applied by the bandage during the course of treatment [2,11]. Therefore, it is important to do the analysis of the interface pressure exerted by the bandaging system for better understanding * Address for correspondence: Mr. Bipin Kumar, Research Scholar, Department of Textile Technology, Indian Institute of Technology, New Delhi 110 016, India. Tel.: +999 024 0340 (mobile); E-mail: bipiniitd18@gmail.com. 0006-355X/12/$27.50 2012 IOS Press and the authors. All rights reserved

2 B. Kumar et al. / Prediction of internal pressure profile of compression bandages Fig. 1. Strain and stress histories in the stress relaxation test. of the compression therapy. Laplace s law is used to calculate the instantaneous localised static internal pressure exerted by a compression system which relates the interface pressure with the tension applied to the bandage, the number of layers wrapped, circumference of limb and the bandage width [1,15,16]. It has been observed from the literatures that the interface pressure decreases over a period of time, hence decreasing the effectiveness of the treatment [2 5,13]. Knowledge of the pressure profile, to which the bandage is exposed during compression therapy, is of theoretical and practical importance in determining the efficacy of the treatment. Continuous measurement of the interface pressure has improved the understanding of compression management and is also very useful for obtaining pressure profile generated by the bandage [4,5]. The decrease in the internal pressure beneath the bandage occurs because of relaxation of the stress in the bandage. The stress relaxation of a material is a viscoelastic property which refers to the behavior of stress reaching a peak and then decreasing or relaxing over time under a fixed level of strain (Fig. 1). Understanding the relaxation behavior in the bandage could be very useful in determining the pressure profile generated by the bandage. The relaxation behavior is described by two basic elements, the spring and the dashpot [6,20]. The spring describes the linear elastic behavior while the dashpot represents the viscous behavior of the Newtonian fluid. By making various combinations of spring and dashpot models, one can simulate the relaxation behavior of fibrous materials such as yarn and fabric [9,14]. Having the above facts in mind, the first part of this paper deals with the relaxation phenomena in the bandage during its application to permanent deformation. Various mechanical models with different combinations of linear or nonlinear spring and dashpot have been used to describe the relaxation behavior of the bandage, as it explains the stress decrease with time under a permanent deformation. In the other part of paper, the pressure profile of bandages has been obtained using a prototype developed. It has been observed that the pressure profile is significantly dependent on the stress relaxation behavior of the bandage. The aim of this work was to determine the pressure profile generated by the bandage using various mechanical models to describe the stress relaxation behavior. 2. Materials and methods 2.1. Bandages It was the aim of this work to do the analysis of short-stretch and long-stretch bandage under same level of extension. Two standard compression bandages (long-stretch and short-stretch) were chosen

Bandage designation B. Kumar et al. / Prediction of internal pressure profile of compression bandages 3 Thickness (mm) GSM ** (g/m 2 ) Table 1 Details of bandages Yarn Tex Ends/cm Picks/cm Extensibility * Warp Weft A 1.26 524.6 53 73 28 72 80 B 1.48 542.5 50 72 28 132 132 * Extensibility is determined by measuring the extension of the bandage when a weight of 10 Newton (N) per cm is applied [4]. ** GSM denotes the gram per square meter. GSM is commonly used scale for fabric weight. (%) Table 2 Results of stress relaxation behavior and pressure profile generated by bandages for 1 h After time Bandage A Bandage B (min) Stress Interface pressure Stress Interface pressure σ e(t)(nm 2 ) P e(t)(nm 2 ) σ e(t)(nm 2 ) P e(t)(nm 2 ) 0 85,556 1600 31,996 666.7 1 71,556 1333 27,811 573.4 5 60,667 1133 26,486 546.7 10 56,000 1027 25,162 540.0 15 54,444 1000 25,162 533.3 20 52,000 986.6 25,162 526.7 30 49,778 973.3 25,162 520.0 45 49,778 946.6 25,162 517.3 60 49,778 933.3 25,162 513.3 Note: Thep-value for the significance test for regression slope is less than 0.01 for both the bandages. with different fabric parameters as listed in Table 1. Both the bandages were made up of cotton yarn in the warp and weft directions, with different values of tensile parameters. Both the bandages were applied slowly to a mannequin limb with 75% extension for pressure measurements. 2.2. Stress relaxation measurements The investigation on the relaxation phenomena was done for the bandages under a constant deformation. Stress relaxation under constant deformation was measured using an INSTRON tensile tester (model-4301). The initial length of the bandage specimen between clamps was 20 cm and the width of the specimen was 5 cm. The bandages were extended up to 75% extension at a fixed rate of extension (200 mm/min). The decrease of the maximal stress was measured after 1, 5, 10, 15, 20, 30, 45 and 60 min (Table 2). The stress relaxation tests for the individual bandages were repeated 5 times and the average values of stresses were used for subsequent analysis. 2.3. Interface pressure measurements The internal pressure profile generated by the bandage was obtained by a prototype which has an online measurement system using differential pressure transmitter and digital process controller that provides a very accurate method of measurement of internal pressure applied by medical bandages. The prototype was based on pneumatic principle which relates the pressure changes in the fluid on application

4 B. Kumar et al. / Prediction of internal pressure profile of compression bandages Fig. 2. Schematic diagram of the pressure measuring system. Bandage designation Table 3 Determination of unknown parameters of mechanical models used for stress relaxation Calculated parameters from mechanical models Maxwell model SLS model Two component Maxwell model with parallel-connect nonlinear spring τ (s) E 1 (Nm 2 ) τ 1 (s) E 1 (Nm 2 ) τ 1 (s) τ 2 (s) b A 3761 44,500 179.4 21,100 814.8 60.6 8.8 B 9015 8900 64.2 9700 63.6 64.2 4.5 Notes: The model parameters are calculated using a nonlinear optimization algorithm. The algorithm used in this study was Levenberg Marquardt algorithm. of an external pressure [4,5]. An air bladder was made and wrapped around the wooden mannequin leg, which was then inflated with air at a particular pressure (P 1 ), and then the bandage was wrapped over the mannequin leg containing the bladders at constant extension. This wrapping exerted some pressure (P ) on the bladder, which was duly observed by the change in the pressure of the air in the bladder and the total pressure (P 2 ) was measured. Then by deducting the initial bladder pressure (P 1 ) from the final pressure reading (P 2 ), the pressure exerted by the bandage was obtained. Figure 2 shows the schematic diagram of the instrument. The pressure profile was obtained after wrapping the bandage at a constant elongation of 75% over the bladder on the mannequin limb having circumference of 43.8 cm. For each individual test, one layer of the bandage was wrapped over the air bladder fixed on the mannequin. The pressure profiles of the individual bandages were obtained 5 times for the same bandage material and the average values of interface pressure were calculated. 2.4. Statistics The linear regression analysis was done to find the correlation between the interface pressures after application of the bandage and the results for the stress relaxation under constant deformation. A p-value less than 0.01 was considered as statistically significant. The fitted parameters of the mechanical models were obtained using optimization fit of unconstrained nonlinear minimization problems in MATLAB (Table 3). The algorithm used in this study was Levenberg Marquardt algorithm. To ensure global convergence, the regression analysis was performed 100 times with different initial guesses for the constants to obtain the minima of the objective function. The guess that produced the lowest minimum was chosen for all subsequent analyses.

B. Kumar et al. / Prediction of internal pressure profile of compression bandages 5 3. Theoretical section: Mechanical models for describing stress relaxation The bandage exhibits viscoelastic properties of a viscoelastic solid, with the elastic properties of a solid, and respond to the Hooke s law and as a viscous liquid as specified by the Newton s law [6,20]. The behavior of stress relaxation in the bandage as a viscoelastic material is described using mechanical models, which consist of the basic model of the spring and the dashpot. We can obtain a number of variations of the basic models such as linear and nonlinear models using different combination of these basic elements [14,18]. Some of the basic models are described below for the explanation of the relaxation phenomena in the bandage. Two mechanical models are taken from the literature while the other model has been derived using various combinations of basic viscoelastic elements: the spring and dashpot. 3.1. Spring and dashpot The spring should be visualized as representing the elastic properties of the bandage according to the Hooke s law, while the dashpot presents the viscous component of the deformation, which is not completely recoverable and time dependent (Fig. 3a) [20]. A Hookean spring is described by Eq. (1): σ s = Eε s, (1) where σ s and ε s are the stress and the strain which are analogous to the spring force and displacement, and the spring constant k is analogous to the elastic modulus E; E has units of N/m 2. The spring model represents the instantaneous elastic response of the material which is completely recoverable. The behavior of the viscous component is described by Newton s law as: σ d = η ε d, (2) where σ d and ε d = d ε d dt, are the stress and the strain rate in the dashpot, respectively, η is the coefficient of viscosity with units of N/m 2 s. The ratio of the coefficient of viscosity to stiffness is a useful measure of the response time of the material s viscoelastic response; this is denoted as: τ = η E. (3) The unit of τ is time, and this ratio is also called as the relaxation time. This ratio helps to determine the viscoelastic response of the material, indicating relaxation time to reach from the old (unrelaxed) to the new equilibrium (relaxed) state of the material [6]. (a) (b) Fig. 3. (a) The spring and the dashpot. (b) Maxwell model.

6 B. Kumar et al. / Prediction of internal pressure profile of compression bandages 3.2. The Maxwell model The Maxwell model represents a material with a linear Hookean spring connected in series with a Newtonian dashpot [6,17]. Because of two elements, the spring and the dashpot are subject to the same stress (σ = σ s = σ d ), the model is also known as an iso-stress model (Fig. 3b). The total strain is sum of the elastic and the viscous strain: ε t = ε s + ε d. (4) In seeking a single equation relating the stress to the strain, it is convenient to differentiate the strain equation and then write the spring and dashpot strain rates in term of the stress: ε t = ε s + ε d = σ E + σ η. (5) Here the bar over the variable denotes time differentiation. In the stress relaxation test, the history of the strain has been assumed as a step function: ε t (t) = ε 0 u(t), u(t) = { 0, t<0, 1, t 0. (6) The Laplace transformation is very convenient in reducing differential equations to algebraic ones. The resulting expression is a function of s, which is written as F (s). Appendix A lists some transform pairs encountered often in these problems. Since, L[ ε t (t)] = ε 0 s, the Laplace transformation of Eq. (5) gives: L(σ) = E (s + 1/τ) ε 0. (7) Since L[ ε t (t)] = ε 0 s, using the inverse Laplace transform, the stress extension relation with the measured value of the stress can be expressed as: σ(t) = Eε 0 e 1/τ = σ 0 e 1/τ. (8) With the known stress σ 0 at t = 0, the unknown parameter τ is determined using the method of least squares. 3.3. Standard linear solid model The Standard Linear Solid (SLS) presents a spring having elastic modulus E 2 in parallel with the Maxwell unit. In this arrangement, the Maxwell arm and the parallel spring experience the same strain (ε = ε E2 = ε M, Fig. 4a). The total stress σ is the sum of the stress in each arm: σ = σ E2 + σ M, (9) ε = ε M = σ M E + σ M η. (10)

B. Kumar et al. / Prediction of internal pressure profile of compression bandages 7 (a) (b) Fig. 4. (a) The standard linear solid (SLS) model. (b) Two-component Maxwell model with parallel-connect nonlinear spring. Since L( ε(t)) = ε 0 s, the Laplace transformation of Eq. (10) gives: L(σ M ) = E 1 (s + 1/τ) ε 0. (11) Using Laplace transformation of Eq. (9): or L(σ) = L(σ E2 ) + L(σ M ) ε 0 ε 0 L(σ) = E 2 s + E 1. (12) (s + 1)/τ 1 So, finally the stress at any time will be, or σ(t) = E 2 + E 1 ε 0 e 1/t 1 σ(t) = σ 0 E 1 ε 0 (1 e 1/t 1 ). (13) With the known stress (σ 0 )andstrainε 0 at t = 0, the unknown parameters E 1 and τ 1 are determined using the method of least squares. 3.4. Two-component Maxwell model with parallel-connect nonlinear spring The derivation for the two-component Maxwell model with parallel-connect nonlinear spring can be derived using Laplace transformation. In this arrangement, each Maxwell arm and the parallel nonlinear spring experience the same strain (Fig. 4b). The total stress σ is the sum of the stress in each arm: σ = σ M1 + σ M2 + σ n. (14) Using the Laplace transformation of Eq. (14): L(σ) = E 1 ε 0 s + 1/τ 1 + E 2 ε 0 s + 1/τ 2 + b ε2 0 s. (15)

8 B. Kumar et al. / Prediction of internal pressure profile of compression bandages The final expression of stress at any time t is given by: σ(t) = E 1 ε 0 e 1/t 1 + E 2 ε 0 e 1/t 2 + bε 2 0. (16) Considering the initial conditions, as for instance: σ 0 = E 1 ε 0 + E 2 ε 0 + bε 2 0, we are looking for the 4 unknown parameters as E 1, τ 1, τ 2 and b. 3.5. Prediction of interface pressure The Laplace law helps to understand a wide range of physiological and pathophysiological processes [1,16]. The localized static pressure exerted on the leg by a compression system can be calculated using modified equation of Laplace s law: P = Tension n R W, (17) where P is the sub-bandage pressure (Nm 2 ), Tension is the longitudinal tension applied to the bandage while wrapping (N), n is the number of layers of the bandage wrapped, R is the radius of the limb (m), W is the bandage width (m). The interface pressure of the compression bandage can be measured using the novel technique described in the literature [21]. The tension in the bandage is related to the longitudinal stress as: Tension = stress area = σ (W h), (18) where h is the thickness of the bandage. The tension in the bandage for a particular extension can be obtained using stress strain behavior of the bandage. So, using the modified Laplace s equation the interface pressure exerted on the leg by a bandage at any time can be calculated as: P (t) = σ(t) h n, (19) R where σ(t) is the longitudinal stress in the bandage. 4. Results The results of the stress relaxation measurement under constant deformation and the correlation of pressure profile with stress relaxation have been presented below. 4.1. Analysis of long-stretch and short-stretch bandage In warp direction the extensibility on bandage B was higher than the bandage A (Table 1). It can be observed from Fig. 7a and b that at the same extension level and keeping the method of wrapping constant bandage A (short-stretch) showed a higher instantaneous interface pressure compared with bandage B (long-stretch). At same level of extension, bandage A also showed high relaxation as compared with bandage B (Fig. 5a and b). The interface pressure drop within 1 h is also higher for bandage A because

B. Kumar et al. / Prediction of internal pressure profile of compression bandages 9 (a) (b) Fig. 5. Results of stress relaxation curves for analysed bandages and the fitted curves from the used mechanical models for 1 h relaxation for the bandages. (a) Bandage A. (b) Bandage B. The investigation on the relaxation phenomena was done for both bandages under a constant deformation (75% elongation). For calculating model constants, initial guess for each constant was multiplied by a random factor between 0.1 and 10 and the regression analysis was performed 100 times to obtain the lowest minima of the objective function. of the higher stress relaxation (Fig. 7a). In both bandages the rate of reduction in pressure is higher for first 15 min and after that the interface pressure remains stable for a long period. 4.2. Analysis of stress relaxation measurements The results of the stress relaxation under constant deformation were measured after 1, 5, 10, 15, 20, 30, 45 and 60 min (Table 2). The analysis of results of the relaxation phenomena indicates that the stress in the bandage decreases at higher rate for the first 15 min, under constant deformation. The fitted parameters of the mechanical models were obtained using optimization fit in MATLAB (Table 3). Using the parameters listed in Table 3 for different mechanical models, the stresses in the bandage were calculated and compared with the experimental values as shown in Fig. 5a and b, where it can be seen that the relaxation phenomena were well described by the higher component model. The two-component Maxwell model with a parallel nonlinear spring showed good agreement with the experimental values. The Maxwell model does not predict the actual behavior of stress relaxation in the bandage. 4.3. Analysis of interface pressure profile generated by the bandage The internal pressure beneath the bandage was obtained using a prototype for 1 h for fixed elongation. Bandages were given 75% elongation and wrap over the bladder on the mannequin limb having circumference of 43.8 cm. The interface pressure decreases with time because of the relaxation of stress happening within the bandage with time. A good correlation was found between the stress relaxation data and the interface pressure for the bandages. The results of interface pressure and stress relaxation data for the bandages are listed in Table 2. The correlation coefficient of the interface pressure and the stress relaxation for the bandages A and B were found to be 0.99 and 0.98, respectively, which shows a linear relationship exists between these two variables. The p-value for the significance test for regression slope is less than 0.01 for both the bandages which indicates the interface pressure is significantly

10 B. Kumar et al. / Prediction of internal pressure profile of compression bandages Fig. 6. Correlation between interface pressure and stress relaxation for bandage A. X-axis represents the values of the longitudinal stress in the bandage A during relaxation testing for 1 h (Table 2). Y -axis represents the values of the interface pressure exerted by the bandage A for 1 h. The correlation coefficient between the interface pressure and the stress relaxation data for bandage A was 0.99. (a) (b) Fig. 7. Results of pressure profile for analysed bandages and the fitted curves from the used mechanical models for 1 h test for the bandages. (a) Bandage A (short-stretch). (b) Bandage B (long-stretch). For each individual test, the bandage specimen was wrapped, over the limb having circumference of 43.8 cm, at a constant elongation (75%). linearly dependent on the relaxation behavior of the bandage. Figure 6 shows the linear relationship between the stress relaxation and the interface pressure. Figure 7 shows the experimental interface pressure and the predicted interface pressure values calculated from the Eq. (18). Analysis of the results for the predicted interface pressure showed the good agreement with the experimental values for the higher component models.

B. Kumar et al. / Prediction of internal pressure profile of compression bandages 11 5. Discussion Compression is still the cornerstone for the treatment of phlebological and lymphatic conditions. The success of this treatment depends on the choice of the bandaging system, the level of pressure applied and sustenance of this pressure during the course of the treatment [10,11]. In this paper an attempt has been made to analyse and model the interface pressure profile generated by the bandage during the course of the treatment. The knowledge of the pressure profile, to which the bandage is exposed during compression therapy, could be used in determining the efficacy of the treatment. To predict the behavior of the pressure profile, we analysed the stress relaxation behavior of the bandage. The relaxation behavior of the bandage can be modelled using two basic elements: the spring and the dashpot [6,14]. The initial deformation in the bandage after loading consists of two elements, the recoverable deformation (elastic deformation) and the deformation, which is recoverable in time. The stress relaxation results of the bandage indicate that the stress in the bandage decreases at higher rate for the first 15 min, under constant deformation (Fig. 5a and b). This is due to the quicker response to the elastic part of deformation in bandages [6]. The comparative analysis of the experimental and calculated values of stress using different mechanical models show that the experimental relaxation curve is closer to that of the mechanical models with more components. The weak point of the multiple component models is the high number of local minima which makes it difficult to find the global minimum [14]. The two-component Maxwell model with parallel-connected nonlinear springs shows the best agreement with the experimental relaxation curve of the analysed bandages. Figure 5 also shows that the Maxwell model does not predict the actual behavior of stress relaxation in the bandage. According to the Maxwell model the stress decreases exponentially to zero, which is not valid for the bandages analysed, as the stress in the bandage become constant after relaxation. The measurement of interface pressure has been done using a prototype designed and developed in our laboratory based on a pneumatic principle. The advantage of this design is the compressibility (softness or resilience) imparted to the mannequin surface due to the presence of the air bladders, giving a model simulating the human leg [4,5]. It was shown that the interface pressure after application of the bandage was highly correlated with the stress relaxation of the bandage under constant deformation (Fig. 6), a linear relationship existing between these two variables. Using the stress relaxation parameters, an attempt was made to predict the behavior of the internal pressure profile generated by the bandage. These two variables could also be related using the Laplace law which relates the tension in the walls of container with the pressure of the container s contents and its radius [1,16]. The results show that the technique used evaluates the pressure profile generated by the bandage during compression very well (Fig. 7a and b). Thus, at the same level of extension, short-stretch bandage A exhibited a higher pressure drop than the long-stretch bandage B (Fig. 7a and b). This is due to higher relaxation in bandage A (Fig. 5a). It was also evident from Fig. 7a and b that, at the same extension level and keeping the method of wrapping constant, short stretch bandage A showed a higher instantaneous interface pressure than long stretch bandage B. This is due to the lower extensibility and higher initial modulus of bandage A compared to bandage B, and hence the higher tension required to give the same level of extension to bandage A than to bandage B. Several limitations must be borne in mind when considering the results of the study. Firstly, in this work all the mechanical models have been used for a certain phase of viscoelastic testing, for example, during stress relaxation only, or for only one level of extension (75%) and fixed strain rate. Many fibrous materials appear to respond differently at different level of extension and strain rate [20]. Future studies

12 B. Kumar et al. / Prediction of internal pressure profile of compression bandages which incorporate the effects of various levels of extension and different strain rates on the relaxation behaviors of the bandages need to done. Secondly, a step strain has been assumed which might be impossible to perform experimentally. Accounting for this limitation may result in a poor prediction for the relaxation behavior of the bandage in giving a ramped strain for longer time. Thirdly, in the present work, long-stretch and short-stretch compression bandages having the same construction and materials have been analyzed. There are other classes of compression bandages having different constructions, such as knitted and woven, as well as those made up of combinations of various fibers, such as PET, nylon, spandex and cotton, that are used for compression therapy. The behavior of these other bandages needs to be studied. Our analysis shows that the pressure profile generated by the bandage could be predicted using stress relaxation parameters. The mechanical models used for describing relaxation phenomena also describe the behavior of the interface pressure with time. Such knowledge of the pressure profile generated by a bandage can improve our understanding of compression management and is also very useful for training purposes in evaluating bandage performance as novel wound care management. Acknowledgement This study was supported by Council of Scientific and Industrial Research, Human Resource Development Group, New Delhi, India. Appendix A: Laplace transformations Basic definitions: L(f(t)) = f(s) = Fundamental properties: 0 f(t)e st dt. L[c 1 f 1 (t) + c 2 f 2 (t)] = c 2 f1 (s) + c 2 f2 (s), ( ) df L = s dt f(s) f(0). Some useful transform pairs: f(t) L(f(t)) = f(s) u(t) 1/s, s>0 1 1/s, s>0 t n n!/s (n+1), s>0 e at 1/(s a), s>a Inverse of the Laplace transform: If F (s) = L{f(t)}, then the inverse transform of F (s) isdefinedas: L 1 {F (s)} = f(t).

Appendix B: List of symbols B. Kumar et al. / Prediction of internal pressure profile of compression bandages 13 Parameter Symbol used Units Stress σ Nm 2 Strain ε Elastic modulus E Nm 2 Coefficient of viscosity η Nm 2 s Relaxation time τ s Interface pressure P Nm 2 Number of bandage layers n Width of bandage W m Radius of the limb R m Thickness of the bandage h m Time t s Variable representing Laplace transformation s References [1] J.R. Basford, The law of Laplace and its relevance to contemporary medicine and rehabilitation, Arch. Phys. Med. Rehabil. 83 (2002), 1165 1170. [2] S.D. Blair, D.D.I. Wright and C.M. Backhouse, Sustained compression and healing of chronic venous ulcers, Br. Med. J. 297 (1988), 1159 1161. [3] A.B. Callam, D. Haiart, M. Farouk, D. Brown, R.J. Prescott and C.V. Ruckley, Effect of time and posture on pressure profiles obtained by three different types of compression, Phlebology 6 (1991), 79 84. [4] A. Das, R. Alagirusamy, D. Goel and P. Garg, Internal pressure profiling of medical bandages, J. Textile Inst. 101 (2010), 481 487. [5] A. Das, B. Kumar, T. Mittal, M. Singh and S. Prajapati, Internal pressure profiling of medical bandages by a computerized instrument, Indian J. Fibre Textile Res. 37(2) (2012), to appear. [6] J. Gersak, D. Sajn and V. Bukosek, A study of the relaxation phenomena in the fabrics containing elastane yarns, Int. J. Clothing Sci. Technol. 17 (2005), 188 199. [7] P.A. Kelly, A viscoelastic model for the compaction of fibrous materials, J. Textile Inst. 102 (2011), 1 11. [8] A.J. Lee, J.J. Dale, C.V. Ruckley, B. Gibson, R.J. Prescott and D. Brown, Compression therapy: effects of posture and application techniques on initial pressures delivered by bandages of different physical properties, Eur. J. Vasc. Endovasc. Surg. 31 (2006), 542 552. [9] H. Liu, X.M. Tao, K.F. Choi and B.G. Xu, Analysis of the relaxation modulus of spun yarns, Textile Res. J. 80 (2009), 403 410. [10] W. Marston and K. Vowden, Position document: understanding compression therapy, in: European Wound Management Association, S. Calne, C. Moffatt and S. Thomas, eds, Medical Education Partnership, London, 2003, pp. 11 17. [11] G. Mosti, V. Mattaliano, R. Polignano and M. Masina, Compression therapy in the treatment of leg ulcers, Acta Vulnologica 7 (2009), 1 20. [12] A. Nelson, Compression bandaging in the treatment of venous leg ulcers, J. Wound Care 5 (1992), 415 418. [13] T.B. Raj, M. Goddard and G.S. Makin, How long do compression bandages maintain their pressure during ambulatory treatment of varicose veins, Br.J.Surg.67 (1980), 122 124. [14] D. Sajn, J. Gersak and R. Flajs, Prediction of stress relaxation of fabrics with increased elasticity, Textile Res. J. 76 (2006), 742 750. [15] J. Schuren and K. Mohr, The efficacy of Laplace s equation in calculating bandage pressure in venous leg ulcers, Wounds UK 4 (2008), 38 47. [16] S. Thomas, The use of the Laplace equation in the calculation of sub-bandage pressure, EWMA J. 3(1) (2003), 21 23. [17] V. Urbelis, A. Petrauskas and A. Gulbiniene, Stress relaxation of clothing fabrics and their systems, Mater. Sci. 13 (2007), 327 332. [18] L. Vangheluwe and P. Kiekens, Modelling relaxation behavior of yarns, Part I: extended, nonlinear Maxwell model, J. Textile Inst. 87 (1996), 296 304. [19] M. Vicaretti, Compression therapy for venous disease, Aust. Prescr. 33 (2010), 186 190. [20] I.M. Ward and D.W. Handley, An Introduction to the Mechanical Properties of Solid Polymers, Wiley, Chichester, 1993. [21] N. Yildiz, A novel technique to determine pressure in pressure garments for hypertrophic burn scars and comfort properties, Burns 33 (2007), 59 64.